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SUPPORT is a collection of programs which complement many of the other programs in the Numerical Solutions Library. With these you will be able to study solutions found with other programs. For instance, if you have a power series produced by one of the DIFFERENTIAL EQUATIONS programs, you can use the POWER SERIES program to study that solution to find its derivatives, roots, integral, maxima and minima. Or you might have a multivariable mixed series produced by one of the APPROXIMATION AND INTERPOLATION programs, then you can use the support programs to find its partial derivatives, multiple integral, maxima and minima, or even evaluate such a series or any of its partial derivatives simultaneously at all points of a rectangular grid. Even the results of the REGRESSION programs can be converted to a form which can be studied to find its (partial) derivatives, (multiple) integral, maxima and minima, or roots.
 
This collection studies multivariable series/regression results: multidimensional grid evaluation, (multiple) integrals, maxima & minima, partial derivatives, roots. Requirements: Windows 98 or later.
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Download Power and Trigonometric Series
Studies one-variable finite power or trigonometric series in a given interval to find roots, maxima & minima, integral, derivatives, graph.
evalgrid.gif (36594 bytes) evgredit.gif (13307 bytes) Download Mixed Series Evaluations
Evaluates a mixed series or any partial derivative at all points of a rectangular grid simultaneously.

Power and Trigonometric Series studies one-variable power or trigonometric series in a given interval to find roots, maxima & minima, integral, derivatives and graph. You can specify the error bound for the results and fully explore intervals to search for multiple solutions. Results can be saved or printed. Includes a help file with instructions, example and methodology.

Mixed Series Evaluations makes it easy to evaluate a multivariable power, trigonometric or mixed series.  It has the ability to evaluate the series or any partial derivative at all points of a rectangular grid at the same time.  You can, for example, have a 300 term series in two variables, X and Y, and you wish to find its value after differentiating, for instance, once with respect to X and twice with respect to Y.  Furthermore, you wish to know this particular partial derivative at all points of a certain rectangular grid which may have, for instance, 700 points.  This program makes it possible to do the evaluation quickly.

Pending programs:

MAXIMA AND MINIMA OF MIXED SERIES is basically the same as the MAXIMA AND MINIMA program of the FUNCTIONS AND EQUATIONS collection, but here our function will be a multivariable mixed series which will be retrieved from a disk file. Such a file may be created by one of the approximation programs or by other means.

MULTIPLE INTEGRATION (CONSTANT LIMITS) AND PARTIAL DIFFERENTIATION OF A MIXED SERIES lets you evaluate, differentiate, or compute multiple integrals with constant limits when the function is a multivariable mixed series.

MULTIPLE INTEGRATION OF MIXED SERIES (VARIABLE LIMITS) is basically the same as the MULTIPLE INTEGRALS program of the FUNCTIONS AND EQUATIONS collection, but here our function will be a multivariable mixed series retrieved from a file. Such a file may be created by one of the approximation programs or by other means.

MIXED POLYNOMIAL AND TRIGONOMETRIC SERIES CREATION creates multivariable power, trigonometric or mixed series in up to 4 variables.  Once the series has been created, it can be studied by other support programs to find multiple integrals, partial derivatives, maxima and minima, or even evaluate such a series or any of its partial derivatives simultaneously at all points of a rectangular grid.

GENERATOR is a program you can use when you wish to generate a one-variable finite power or trigonometric series and you know the general term which generates the coefficients.

REORDERING OF MIXED SERIES reorganizes any multivariable power, trigonometric or mixed series in up to 4 variables. As has been pointed out, the variables in such a series may be rearranged. For example, in a 2-variable power series in X and Y, either one may be specified as the outermost or innermost variable and the resulting polynomial should be the same. The order is simply the order in which you entered them when you ran the approximation or creation program. If each variable is specified in the same manner, you may enter their order in different ways but we should expect the coefficients corresponding to each term to be the same. This is indeed the case, although there may be small variations because the computations are performed in a different order. For instance, if we have a polynomial in X and Y, we may organize it as

(A0+B0*X+C0*X^2)+(A1+B1*X+C1*X^2)*Y+(A2+B2*X+C2*X^2)*Y^2

where X is the innermost variable and Y the outermost, or as

(A0+A1*Y+A2*Y^2)+(B0+B1*Y+B2*Y^2)*X+(C0+C1*Y+C2*Y^2)*X^2

where Y is the innermost variable and X the outermost.

The purpose of this program is to reorganize such series because sometimes it is necessary, for instance when interchanging the order of integration in a multiple integral with variable limits.

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